Water utility managers employ a variety price and non-price policies to induce conservation as a way to defer expensive capacity expansion and to overcome scarcity during periods of drought. Economists tend to focus on financial motivations for consumers, but there is a growing literature in economics and other related fields that explores the potential for other sources of motivation to be harnessed to achieve policy outcomes. Knowing the relative effectiveness and the trade-offs associated with such approaches can help planners to make more efficient policy.

This dissertation investigates the effect of financial and social incentives on water conservation by studying multiple policy approaches used by a water utility in the Reno metropolitan area to promote conservation in the context of a historic drought in the southwestern U.S. In the first chapter, I investigate how providing better price information on monthly utility bills can promote consumer response to financial incentives for water conservation. I provide empirical evidence of consumer inattentiveness to prices, and discuss how this behavior can undermine price schedules that are designed in part to promote conservation. In the second chapter, I focus once again on consumer inattentiveness to prices and consumption behavior, but I analyze a treatment that lowers price salience rather than increases it. I examine enrollment in automatic bill payment and paperless billing programs, which can encourage consumers to become inattentive to recurring charges and thus less aware when changing consumption habits lead to increased water bills. These programs have the unintended consequence of encouraging consumers to be less attentive to prices, which further undercuts the response to conservation incentives built into price schedules. In the final chapter, I turn from financial incentives for water conservation to how social incentives can be used to promote conservation using a field experiment to test the impact of providing normative comparisons on conservation during a drought.

Consumers often face complex pricing schemes when making purchasing decisions. Inefficiencies arise when such schemes are not fully understood. Electric and water utilities use increasing block tariffs (IBT’s) to promote conservation. However, recent evidence suggests that consumers may not respond to the marginal price under these price systems. The first chapter of this dissertation investigates price salience as a possible mechanism by leveraging quasi-exogenous variation in the level of price-related information provided to households on their monthly water bills. I exploit a merger between the two water utilities in Reno that occurred in 2015. Before the merger, one group of households received information on monthly bills about the IBT price schedule, while the other did not; after the merger, both groups received price information. Using a difference-in-differences approach, I find that providing consumers with bills containing better price information leads to a more than 3\% decrease in average water consumption, suggesting that salience is important. I develop a model of consumer decision-making under price uncertainty that predicts consumers will have a differential response to information based on where their consumption is relative to the block tariff threshold. When estimating the effect of information by historical consumption level, I find empirical evidence consistent with these predictions.

The second chapter investigates how automatic and paperless billing enrollment affect residential water demand using a difference-in-differences approach. I find that enrolling in automatic bill payment (ABP) leads to a 2-3\% increase in average water consumption while paperless (PL) enrollment leads to a 1\% increase in water consumption. I also shed light on the relationship between income effects and changes in consumption after enrollment by estimating heterogeneous treatment effects by quintiles of the distribution of property values. I find that average treatment effects do not significantly vary across the income distribution, which indicates that the increase in consumption from ABP enrollment is due to consumer inattentiveness rather than changes in income. I also consider how enrollment in ABP and PL can affect subsequent participation in voluntary conservation programs. ABP customers consume an additional 6\% more than non-ABP customers during when voluntary drought restriction are implemented. Overall, there is evidence that enrollment in these programs promotes consumer inattentiveness to prices as well as utility communications, which undermines financial and social incentives designed to promote conservation.

The final chapter investigates how normative appeals for water conservation drive behavioral change using a large-scale, randomized field experiment. Using a new social comparison that reduces the correlation between pre-treatment consumption and the difference from the peer group, we isolate the impact of the normative component of the message. The strength of the message, defined as a household's performance relative to a peer group, is a primary driver of social comparisons' efficacy, consistent with social comparisons imposing a moral cost on excess consumption. Relative to a nudge that highlights financial savings, social comparisons generate less persistent water savings and are more dependent on sending multiple mailers. While moral motivations are likely driving behavioral change in response to normative appeals, there are opportunities to improve welfare by designing messages that prompt consumers to address mis-optimization of water consumption. This chapter is joint work with Daniel Brent, Joe Cook, Kimberly Rollins, Shawn Stoddard, and Michael Taylor.

Perelman stated without proof that a 3-dimensional compact Riemannian manifold which is locally volume collapsed, with respect to a lower curvature bound, is a graph manifold. The theorem was used to complete his Ricci flow proof of Thurston’s geometrization conjecture. Kleiner and Lott gave a proof of the theorem as a part of their presentation of Perelman’s proof.

In this dissertation, we generalize Kleiner and Lott’s version of Perelman’s theorem to 4-dimensional closed Riemannian manifolds. We show that under some regularity assumptions, if a 4-dimensional closed Riemannian manifold is locally volume collapsed then it admits an F-structure or a metric of nonnegative sectional curvature.

Originally developed in the 1950s, Kolmogorov--Sinai entropy is a very powerful isomorphism invariant for measure-preserving systems that measures the ``complexity'' or ``randomness'' of a system. There is also a relative version of this notion which measures the additional complexity of a system when compared to a fixed reference system. In 1997, Katok--Thouvenot and Ferenczi independently introduced a notion of ``slow entropy'' as a way to quantitatively compare measure-preserving systems with zero Kolmogorov--Sinai entropy. The goal of this thesis is to develop a relative version of this theory and apply it to several other natural dynamical questions.

Chapters 1 and 2 lay out the definition and basic properties of relative slow entropy. Our definition inherits many desirable properties that make it a natural generalization of both the Katok--Thouvenot/Ferenczi theory and the classical conditional Kolmogorov--Sinai entropy. In Chapter 3, we address the question: under what conditions is a generic extension of a system also isomorphic to the base system? Using relative slow entropy as a tool to prove systems non-isomorphic, we show that a generic extension is not isomorphic to the base system whenever the base has zero Kolmogorov--Sinai entropy. Chapter 4 concerns the well-studied notions of isometric and weakly mixing extensions. We give necessary and sufficient entropy-theoretic conditions for extensions to be isometric or weakly mixing. Finally, Chapter 5 investigates the notion of rigidity. Although there is a well known definition for what it means for a single system to be rigid, there is no standard definition for the notion of a rigid extension. We provide a new candidate definition and investigate its consequences. We show that rigid extensions are generic and give an entropy-theoretic sufficient condition for an extension to be rigid. As a consequence, we obtain a new entropy-theoretic characterization of rigid systems which may be of independent interest.

Gene expression is a multi-step process that is fundamental to all cellular activities. In Drosophila oogenesis and embryogenesis both RNA localization and transcription are highly regulated and critical for proper development of the embryo. During oogenesis, maternal RNAs spatially localized within the oocyte. A few localized maternal mRNAs that are required for the proper axial patterning of the embryo have been well-studied. However, a large proportion of the genome is expressed in the ovary and deposited into the embryo. These maternally derived RNAs and proteins drive the earliest events of embryogenesis before the zygotic genome is activated and gene products derived from the zygotic genome take over the control of development. Both maternal RNA localization and early embryo gene expression have undergone substantial changes over the course of evolution in Diptera between species of different genera. However, little was previously known about the evolutionary dynamics of mRNA localization and early gene expression on shorter timescales within a genus or within a species. In this dissertation I determine the extent of natural variation in maternal and zygotic RNA complements within and between populations of a single species, Drosophila melanogaster. Additionally, I examine how maternal RNA localization changes have occurred within the Drosophila genus. In the first chapter of this dissertation, I utilize two geographically distinct populations of Drosophila melanogaster with known differences in genomic variation to examine the natural variation of maternal and zygotic transcripts within and between populations of a single species. I find that maternal gene expression has higher conservation than zygotic gene expression, similar to what has been found when comparing different species of Drosophila. Overall, there is more expression variation within populations than fixed expression differences between them. Furthermore, I find an increase in differential expression of maternal and zygotic transcriptomes within the Zambia population, a population with higher genomic variation, than the Raleigh population. I find that some of the most differentially expressed genes between populations are genes with known selection signatures corresponding to the out-of-Africa expansion of D. melanogaster. Additionally, I find an enrichment of differentially deposited mRNAs between populations on the X chromosome at stage 2, when all transcripts are a product of an XX genotype. In summary, I find that the demographic history of D.melanogaster has shaped the maternal and zygotic mRNA complements between populations of the species. In the second chapter, I present a study on differences in RNA localization along the Drosophila phylogeny. To determine the identity of localized maternal mRNAs, I bisect stage 14 oocytes from five species of Drosophila and sequenced mRNAs from the anterior and posterior halves and then performed differential expression analysis. I find several differences in localization between species. I categorize changes in localization in two categories. First, transcripts that are localized in a subset of species, while having no maternal deposition in others. This indicates lineage specific transcription as well as localization. And second, genes that are maternally deposited in all five species with enrichment to the anterior or posterior in only a subset of these species. I hypothesize that gains and losses of mRNAs could be due to new deposition of transcripts already equipped with cis-regulatory elements able to associate with localization machinery or a gene with pre-existing maternal expression that undergoes changes in regulatory elements that confer the ability to be localized. Overall, this dissertation shows that even within short evolutionary timescales there exists variation in early embryonic gene expression and mRNA localization, both critical to early development.

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The precise regulation of gene expression is especially important during the earliest stages of development, when critical processes lay the foundation for the rest of development. At this time, embryogenesis is dependent on the transcriptional products of two genomes, from the mother and the zygote. Maternally deposited transcripts are supplied to the oocyte during oogenesis and carry out all initial developmental processes from the beginning of embryogenesis until the zygotic genome is activated. Over time, new transcripts are produced from the zygote as maternally deposited transcripts are degraded. The coordinated handoff of developmental control from the maternal to the zygotic genome is tightly regulated and highly conserved. In my dissertation, I investigate two aspects of gene regulation during early development and ask how they compare and evolve across species of Drosophila. In Chapter 1, I looked at how gene regulation evolves for differentially maternally deposited and zygotically transcribed genes by using hybrid crosses between three closely related species, D. simulans, D. sechellia, and D. mauritania. Surprisingly, the mechanisms of gene regulatory change differed substantially between the maternal and zygotic genome. There were more differences in maternal deposition resulting from changes in trans regulation while differences in zygotic transcription resulted from a combination of cis, trans, and the joint action of cis and trans changes. This is indicative that the maternal and zygotic genomes are under different sets of regulatory constraints and likely evolve via different mechanisms. Another critical aspect of gene regulation that I address in my dissertation is the trajectory of maternal transcript degradation throughout development, until all maternal transcripts are degraded, and how it compares across species of Drosophila. We chose four species of Drosophila, D. melanogaster, D. persimilis, D. virilis, and D. yakuba, which vary in developmental time and geographic origin and represent a range of divergence times. Looking at transcripts that are maternally transcribed and not later transcribed by the zygote (maternal-only), we found that a similar proportion degrades by the end of stage 5 in each of the species examined. This suggests that maternal transcripts are stable for a longer absolute amount of time in species that develop more slowly. We also find that relatively few maternal-only transcripts are common across all species examined while a larger proportion are unique to a specific species, indicating a lack of conservation of maternal-only genes, which is especially surprising given the high degree of conservation of maternal genes overall. Future work will investigate whether these transcripts, particularly those that degrade later in development than have previously been examined, contain motifs that may act as signatures for degradation and look at how those compare across species. Overall, the work in this dissertation gives a better understanding of transcriptional and post-transcriptional gene regulation during early embryogenesis and how it evolves across species of Drosophila.

We study the Ricci flow on Riemannian groupoids. We assume that these groupoids are closed and that the space of orbits is compact and connected. We derive maximum principles for groupoids and give some applications for immortal Ricci flow solutions on closed manifolds. We prove the short time existence and uniqueness of the Ricci flow on groupoids. We also define a F-functional and derive the corresponding results for steady breathers on these groupoids.